Question: The geometric sequence $(a_i)$ is defined by the formula: $a_i = -\dfrac{2}{3} \left(3\right)^{i - 1}$ What is $a_{4}$, the fourth term in the sequence?
Solution: From the given formula, we can see that the first term of the sequence is $-\dfrac{2}{3}$ and the common ratio is $3$ To find $a_{4}$ , we can simply substitute $i = 4$ into the given formula. Therefore, the fourth term is equal to $a_{4} = -\dfrac{2}{3} \left(3\right)^{4 - 1} = -18$.